Generalized sectional convergence and multipliers
type: Item
instance of: scholarly article
title: Generalized sectional convergence and multipliers
zbMATH Open document ID: 0881.46010
author: Stephen A. Saxon
author: William H. Ruckle
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-02-19T00:00:00Z
review text: A generalized sectional convergence scheme (gscs) is defined as a sequence \((T_n)\) of infinite matrices with the following properties: (1) Each \(T_n\) has finitely many nonzero entries, (2) for each \(i\), \(j\), \(\lim_{n\to\infty} T_n(i, j)=\delta_{ij}= \begin{cases} 1,(i=j)\\ 0,(i\neq j)\end{cases}\). Some of the results of this paper are: (1) If \(S\) is a barrelled \(AK(T_n)\) space, then \(S\) has the \(\beta\varphi\) topology. (2) Let \((T_n)\) be a gscs and let \(\Theta\) be a subspace of \(\ell^1\). Let \(\Lambda\) denote the largest subspace of \(\ell^1\) such that, setwise, \(\Lambda(T_n)= \Theta(T_n)\). The normed space \(\Lambda(T_n)\) is barrelled if and only if \(\Lambda\) is a barrelled subspace of \(\ell^1\). The paper also contains some multiplier theorems.
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46A08
Mathematics Subject Classification ID: 47B37
zbMATH DE Number: 811198
zbMATH Keywords: multplier spaces
zbMATH Keywords: generalized sectional convergence scheme
zbMATH Keywords: barrelled
zbMATH Keywords: \(\beta\varphi\) topology
zbMATH Keywords: barrelled subspace
zbMATH Keywords: multiplier theorems
reviewed by: K. Chandrasekhara Rao
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1261
OpenAlex ID: W1972244766
DOI: 10.1006/JMAA.1995.1261
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description: scientific article; zbMATH DE number 811198